(x-1)*(x+9)=7*(2x+1)

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Solution for (x-1)*(x+9)=7*(2x+1) equation: 


Simplifying
(x + -1)(x + 9) = 7(2x + 1)

Reorder the terms:
(-1 + x)(x + 9) = 7(2x + 1)

Reorder the terms:
(-1 + x)(9 + x) = 7(2x + 1)

Multiply (-1 + x) * (9 + x)
(-1(9 + x) + x(9 + x)) = 7(2x + 1)
((9 * -1 + x * -1) + x(9 + x)) = 7(2x + 1)
((-9 + -1x) + x(9 + x)) = 7(2x + 1)
(-9 + -1x + (9 * x + x * x)) = 7(2x + 1)
(-9 + -1x + (9x + x2)) = 7(2x + 1)

Combine like terms: -1x + 9x = 8x
(-9 + 8x + x2) = 7(2x + 1)

Reorder the terms:
-9 + 8x + x2 = 7(1 + 2x)
-9 + 8x + x2 = (1 * 7 + 2x * 7)
-9 + 8x + x2 = (7 + 14x)

Solving
-9 + 8x + x2 = 7 + 14x

Solving for variable 'x'.

Reorder the terms:
-9 + -7 + 8x + -14x + x2 = 7 + 14x + -7 + -14x

Combine like terms: -9 + -7 = -16
-16 + 8x + -14x + x2 = 7 + 14x + -7 + -14x

Combine like terms: 8x + -14x = -6x
-16 + -6x + x2 = 7 + 14x + -7 + -14x

Reorder the terms:
-16 + -6x + x2 = 7 + -7 + 14x + -14x

Combine like terms: 7 + -7 = 0
-16 + -6x + x2 = 0 + 14x + -14x
-16 + -6x + x2 = 14x + -14x

Combine like terms: 14x + -14x = 0
-16 + -6x + x2 = 0

Factor a trinomial.
(-2 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-2, 8}

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